Finite Group Databasebeta

← C5×#4294⋊AGL(1,𝔽5) #30685534

Subgroups — C5×#4294⋊AGL(1,𝔽5) #30685534

Order 17100.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D5×#4294C211yesmaximal, characteristic
2C3×C5×C19⋊AGL(1,𝔽5)C311yesmaximal, characteristic
3C52×#4294C411yescharacteristic, complemented, Hall
4#4294⋊AGL(1,𝔽5)C511yesmaximal, characteristic, direct product factor
5C5×#4294⋊C4—51nomaximal
6C3×C5×D5×C19C2×C311yescharacteristic
7C5×C19⋊AGL(1,𝔽5)C911yescharacteristic, complemented, Hall
8C2×C5×#4294—51no—
9D5×#4294C2×C511yescharacteristic
10C3×C52×C19C3×C411yescharacteristic
11C3×C19⋊AGL(1,𝔽5)C3×C511yescharacteristic
12C3×C5×Dic19—51no—
13C5×D5×C19C2×C911yescharacteristic
14C5×C9×AGL(1,𝔽5)—191nomaximal, Hall
15C5×#4294—41no—
16C5×#4294C4×C511yescharacteristic, complemented
17C5×#4294AGL(1,𝔽5)11yescharacteristic, complemented
18#4294⋊C4—51noHall
19C2×C3×C5×C19—51no—
20C3×D5×C19C2×C3×C511yescharacteristic
21C52×C19C4×C911yescharacteristic, complemented, Hall
22C5×C9×D5—191no—
23C19⋊AGL(1,𝔽5)C5×C911yescharacteristic, complemented
24C5×Dic19—51no—
25C2×#4294—51no—
26C3×C5×AGL(1,𝔽5)—571no—
27C3×C5×C19—41no—
28C3×C5×C19C3×C4×C511yescharacteristic
29C3×C5×C19C3×AGL(1,𝔽5)11yescharacteristic
30C3×Dic19—51no—
31C52×C9—191noHall
32C2×C5×C19—51no—
33D5×C19C2×C5×C911yescharacteristic
34C9×AGL(1,𝔽5)—191no—
35C4×C5×C9—951no—
36#4294C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
37C3×C5×D5D19⋊C311yescharacteristic
38C2×C3×C19—51no—
39C5×AGL(1,𝔽5)—571noHall
40C5×C19—41no—
41C5×C19C4×C5×C911yescharacteristic, complemented
42C5×C19C9×AGL(1,𝔽5)11yescharacteristic, complemented
43C2×C5×C9—951no—
44C9×D5—191no—
45Dic19—51noHall
46C3×C52(C19⋊C3)⋊C411yescharacteristic
47C3×AGL(1,𝔽5)—571no—
48C3×C4×C5—2851no—
49C3×C19C3×C5×AGL(1,𝔽5)11yescharacteristic
50C5×D5#4294⋊C211yescharacteristic
51C5×C9—191no—
52C5×C9—191no—
53C5×C9—761no—
54C2×C19—51no—
55C4×C9—951noHall
56C2×C3×C5—51no—
57C3×D5C5×D19⋊C311yescharacteristic
58C52#4294⋊C411yescharacteristic, complemented, Sylow
59AGL(1,𝔽5)—571no—
60C4×C5—2851no—
61C19C5×C9×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
62C2×C9—951no—
63C3×C5—41no—
64C3×C5C5×(C19⋊C3)⋊C411yescharacteristic
65C3×C5(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic
66C3×C4—2851no—
67C2×C5—51no—
68D5C5×#4294⋊C211yescharacteristic
69C9—191noSylow
70C2×C3—51no—
71C5—41no—
72C5C5×#4294⋊C411yescharacteristic, complemented
73C5#4294⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
74C4—2851noSylow
75C3C5×(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic
76C2—51no—
subgroupG/H
center, hypercenterC3×C5(C19⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C4×C5×C9
FrattiniC3C5×(C19⋊C3)⋊AGL(1,𝔽5)
Fitting, socleC3×C52×C19C3×C4
prime radicalC3×C5×D5×C19C2×C3
cosocleC3×D5×C19C2×C3×C5
LCSG ▷ C5×C19
UCSC1 ◁ C3×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C52×#4294C4semidirect
4. #4294⋊AGL(1,𝔽5)C5direct (N × H)
7. C5×C19⋊AGL(1,𝔽5)C9semidirect
16. C5×#4294C4×C5semidirect
17. C5×#4294AGL(1,𝔽5)semidirect
21. C52×C19C4×C9semidirect
23. C19⋊AGL(1,𝔽5)C5×C9semidirect
36. #4294C5×AGL(1,𝔽5)semidirect
41. C5×C19C4×C5×C9semidirect
42. C5×C19C9×AGL(1,𝔽5)semidirect
58. C52#4294⋊C4semidirect
61. C19C5×C9×AGL(1,𝔽5)semidirect
72. C5C5×#4294⋊C4semidirect
73. C5#4294⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×D5×#42942
C3×C5×C19⋊AGL(1,𝔽5)3
#4294⋊AGL(1,𝔽5)5
C5×#4294⋊C45
C5×C9×AGL(1,𝔽5)19